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In this paper we obtain a general statement concerning pathwise convergence of the
full discretization of certain stochastic partial differential equations (SPDEs) with nonglobally
Lipschitz continuous drift coefficients. We focus on non-diagonal colored noise
instead of the usual spaceï¿½??time white noise. By applying a spectral Galerkin method for
spatial discretization and a numerical scheme in time introduced by Jentzen, Kloeden and
Winkel we obtain the rate of path-wise convergence in the uniform topology. The main
assumptions are either uniform bounds on the spectral Galerkin approximation or uniform
bounds on the numerical data. Numerical examples illustrate the theoretically predicted
convergence rate.
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